To operate a technical system, such as a water network or a power supply network, for example, optimization algorithms or mathematical optimization methods are frequently employed. The optimization algorithms are used in order to achieve a predetermined target, in particular to minimize or maximize the target function. For the example of a water network, the target function may relate, by way of example, to the minimization of a power consumption for the pumps and treatment of the water. The optimization algorithm is used to optimize particular controlled variables that are used to adjust the controllable components of the technical system, for example pumps and valves of the water network. The optimization can be used to generate control plans for all the controllable processes or components in the network-like system, frequently for a relatively short optimization period, for example of 24 hours.
In order to be able to provide suitable control plans, the optimization algorithm needs to take into consideration a few technical constraints or secondary conditions, for example particular limit values for the controllable components, such as pumps or valves. Further examples thereof are minimum or maximum values of system variables, such as e.g. predetermined threshold values for capacities of processing steps for the water or minimum or maximum fill levels of reservoirs for the example of a water network. Many of these conditions can be evaluated directly or else within a short optimization period of, by way of example, 24 hours. However, constraints or secondary conditions also exist that necessitate a larger observation horizon, for example of a few weeks, months or years. Examples of long-term secondary conditions of this kind are production targets, such as a particular flow of water per month or maximum operating periods for pumps per month or year. Long-term secondary conditions of this kind cannot be modeled by conventional constraints within a contrastingly shorter optimization period. A simple approach to take into consideration long-term secondary conditions is to expand the optimization period to this long-term period. However, this disadvantageously results in a lengthened execution time for the optimization algorithm that, by way of example, may even be too long in some applications.
A further conventional approach to process long-term secondary conditions is to transform them into simple hard constraints within the shorter optimization period. This can be realized by simple arithmetic operations or stochastic distributions. However, these approaches have the disadvantage of not always being able to provide the best solution for the operation of the water network over the whole control period.